The Articles.
After searching for articles containing the appropriate sample size, I finally came to choose articles about David Beckham’s performance in a Manchester United game. I figured out that Tabloid’s in general comment on Sport in more detail than the rest of the news (in particular).
Data Representation.
To analyse the spread of the data collected, I will interpret the findings into various graphs and diagrams, and then write a ‘mini conclusion’ on what the information shows and why I chose that particular method of displaying the results. Below is a brief summary of the methods I intend to use.
Stem and Leaf Diagrams – This shows clearly the modal and median sentence lengths and makes the calculations of the Mean and Range of the sentence lengths easier.
Cumulative Frequency Diagrams – this method simplifies the calculation of the upper, lower and inter-quartile range. Furthermore, this displays the data needed to construct a Box and Whisker Plot.
Box and Whisker Plots – This shows whether the middle of the sample is symmetrical about the mean. This also contains the Mean, Median, Mode, Range and Quartiles, as in the Cumulative frequency Diagrams.
Pie Charts – This illustrates the frequency of sentence lengths and also provides a different format to bar charts and line graphs.
Bar and Frequency Polygons – As mentioned, these illustrate the same information as the pie charts, but do show specific frequency values.
Histograms – This shows the dispersion of Sentence lengths and also enables the standard deviation to be displayed.
Standard Deviation – I have chosen to use this as it shows the spread of the data and whether or not the data is positively or negatively skewed.
Investigation
I have drawn up two tables showing the results obtained from counting each of the sentence lengths from each newspaper. You can find this labelled – Table 1.hjgjhgjhgjhghjghjghjghjgjhgjhgjhgjhghjghjghjghjghjgg
To begin with, I will calculate the Mean, Median, Mode and Range from each paper. The mean can be calculated exactly, it makes use of all the data and can be used in further statistical calculations, however it can be misleading in the event of a very high value of a very low value. As the data is ungrouped at the moment, I will construct a Stem and Leaf diagram and then calculate the averages.
Below is a Stem and Leaf diagram containing both sets of data from each newspaper, in the order of which they appeared in the article.
Stem and Leaf Diagram
Sun (raw data):
02, 09, 21, 25, 32, 20, 49, 19, 25, 13, 29, 36, 27, 24, 10, 25, 34, 31, 44, 07, 20, 30, 28, 30, 30, 36, 17, 30, 06, 32, 36, 30, 17, 16, 25, 06, 08, 32.
Guardian (raw data):
04, 05, 14, 42, 53, 30, 35, 33, 22, 21, 20, 05, 20, 10, 23, 02, 22, 12, 30, 26, 12, 18, 46, 18, 24, 17, 28, 40, 28, 15, 09, 33, 25, 24, 25, 23, 03, 24.
I will now insert the data into a Stem and Leaf Diagram -
The Sun The Guardian
8, 6, 6, 7, 9, 2 0 4, 5, 5, 2, 9, 3
6, 7, 7, 0, 3, 9 1 4, 0, 2, 2, 8, 8, 7, 5
5, 8, 0, 5, 4, 7, 9, 5, 0, 5, 1 2 2, 1, 0, 0, 3, 2, 6, 4, 8, 8, 5, 4, 5, 3, 4
2, 0, 6, 2, 0, 6, 0, 0, 1, 4, 6, 2 3 0, 5, 3, 0, 3
4, 9 4 2, 6, 0
5 3
The above diagram shows that there are longer sentence lengths in the Sun as far as 30 words are concerned, however, this brings new information to light. As I had expected, the data has a roughly normal distribution, in the Guardian. To highlight this further I will draw frequency density graph at a later stage. The guardian consists of a sentence containing more than 50 words. This may or may not affect its mean.
As mentioned, I will calculate the mean, median, mode and range for each newspaper.
The Sun
Total words in 38 sentences: 881
I have decided calculate the mean in the order the numbers are shown on the Stem and Leaf Diagram.
Mean = 2 + 9 + 7 + 6 + 6 + 8 + 19 + 13 + 10 + 17 + 17 + 16 + 21 + 25 + 20 + 25 + 29 + 27 + 24 + 25 + 20 + 28 + 25 + 32 + 36 + 34 + 31 + 30 + 30 + 36 + 30 + 32 + 36 + 30 + 32 + 49 + 44 = 881
38 = A mean of 23 (to 1 d.p.)
Mean: 23 words
To save time in writing out the numbers numerically (for the Median), I have taken the data from table 1.
Median: 25 words
Mode : 30 words
Range : 47 words (49 – 02 = 47)
Mini-conclusion.
Although the modal sentence value is moderately high, the mean and the median are quite close together. The high range suggests that the lengths of sentences in the Sun are not of a constant value.
The Guardian
Total words in 38 sentences: 841
Again, I have decided calculate the mean in the order the numbers are shown on the Stem and Leaf Diagram.
Mean = 4 + 5 + 5 + 2 + 9 + 3 + 14 + 10 + 12 + 12 + 18 + 18 + 17 + 15 + 22 + 21 + 20 + 20 + 23 + 22 + 26 + 24 + 28 + 28 + 25 + 24 + 25 + 23 + 24 + 30 + 35 + 33 + 30 + 33 + 42 + 46 + 40 + 53 = 841
38 = A mean of 22 (to 1 d.p.)
Mean: 22 words
Again, to save time in writing out the numbers numerically (for the Median), I have taken the data from table 3.
Median: 22 words
Mode: 24 words
Range: 51 words (53 – 02 = 51)
The Range was found by subtracting the largest number away from the smallest number in each case.
Mini-conclusion.
This is somewhat similar to the Tabloid. The modal sentence length is again higher than the mean and the median values, and similarly, the range is very high at 51. Compared to the results gathered from the tabloid, the broadsheet appears to have a more consistent sentence length, and I will prove this when constructing a histogram.
Cumulative Frequency Diagrams.
I will now construct a Cumulative Frequency Table and Diagram. In order for me to do this, I need to group the data accordingly. Below is a sample of how the data will be grouped this applies for both papers:
0 < w ≤ 10 30 < w ≤ 40
10 < w ≤ 20 40 < w ≤ 50
20 < w ≤ 30 50 < w ≤ 60*
* This group applies only to the broadsheet newspaper
The Sun
Cumulative Frequency Diagram for the Tabloid newspaper
The Guardian
Cumulative Frequency Diagram for the Broadsheet
Now I will construct a Comparative Cumulative Frequency Diagram displaying the two sets of data. This can be found below.
Comparative Cumulative Frequency Diagram displaying the two sets of data.
Now, as the data is in a grouped frequency, the mean is calculated using the midpoints of each group. The midpoints have been calculated in the table below.
The Sun
(5 x 7) + (15 x 7) + (25 x 14) + (35 x 8) + (45 x 2) = 860
38 = A mean of 23 (to 1 d.p.)
Median = 20 < w < 30
Mode = 20 < w < 30
Box and Whisker Plot showing information from the Tabloid.
The Guardian
(5 x 7) + (15 x 9) + (25 x 15) + (35 x 4) + (45 x 2) + (55 x 1) = 830
38 = A mean of 22 (to 1 d.p.)
Median = 20 < w < 30
Mode = 20 < w < 30
Box and Whisker Plot showing the data from the Broadsheet.
Comparative Box and Whisker Plot
Mini Conclusion
It is clear that by using grouped data, the Median and Mode fall under the same group for each newspaper. The Braodsheet and Tabloid Data is negatively skewed Also, the mean for the Tabloid is still slightly higher than the Broadsheet, as it was when the data was ungrouped. Also, the sample of sentences from the Sun has a larger mean than the sample taken from the Guardian, suggesting that the sentences, on average are longer in the Sun, however this evidence is not conclusive, so further calculations have to be made.
I will now display a Cumulative frequency Diagram and Box Plot containing both sets of data.
This shows that the Sun has a more consistent sentence length than the Guardian. The Sun has a smaller range and Inter-quartile Range; the cumulative frequency diagram shows the Sun to have a steeper ogive than the Guardian, also suggesting consistency.
Pie Charts
In order for me to construct a pie chart, I will use the following formulae:
360(º) / 38 (total sentences) = 9.47, therefore
1º = 9.47 x n = nº
Tabloid
Pie-chart for the tabloid newspaper.
Mini-conclusion
This shows that the modal sentence length is 20 < w ≤ 30. This group is in the middle of the five groups suggesting that the sentence lengths are a consistent value. The remaining four groups prove this, the groups on either side (10 < w ≤20 and 30 < w ≤ 40 slightly lower than the 20 < w ≤ 30 group, and it is true for the other groups.
Below is the table containing the data needed to construct a pie chart for the Broadsheet newspaper.
Broadsheet
Pie Chart for the Broadsheet’s data.
Mini-conclusion.
Similarly to the previous Chart, the modal sentence length is 20 < w ≤ 30. When compared to the Tabloid, this has one more group, which shows that the broadsheet is not as consistent.
Bar charts and Frequency Polygons
I have decided to construct simple Bar charts along with Frequency polygons. I have collected together the information from each article and constructed simple frequency tables, below.
Tabloid
Bar chart and frequency polygon for the Tabloid newspaper
Broadsheet
Bar chart and frequency polygon for the broadsheet Newspaper.
Now, to enable me to compare each chart, I will draw the two charts onto one diagram – making it easier to compare.
Comparative Bar Chart and Frequency Polygon
Mini-conclusion.
This shows that the pattern of frequencies in the Sun is more balanced than in the Guardian. The frequency polygon has low frequencies in the low groups and high groups, leaving the middle values with a high frequency.
Histograms.
From the collected data, I will calculate the frequency density to illustrate the dispersion of the data.
To find the frequency density, I will use the following formula:
Frequency Density = Frequency
Width of Class Interval
Again I will use grouped frequencies to make the graph more appropriate and less confusing to analyse.
Tabloid
Histogram showing the Frequency Density for the Tabloid Newspaper.
Broadsheet
Histogram containing the frequency density of the Broadsheet.
Now, I will draw another histogram containing both sets of data, ready for comparison.
Comparative Histogram containing both sets of data.
Mini-conclusion
This clearly shows that the majority of sentence lengths in the two papers lie between 0 < w ≤ 10 and 20 < w ≤ 30 words, and are in the lower three groups. This loner the sentences have a relatively small frequency density, than the smaller sentence groups. However, this is more obvious for the tabloid, showing that the Sun tends to use smaller sentences, in a slight comparison to the Guardian.
Standard Deviation.
I will calculate the standard deviation to show the spread of the data, to do this again I will use a formula, shown below:
Standard Deviation
So first of all I will find the midpoints.
Total 860
Mean = 860 / 38 = 22.63
Now that I have found the mean, I can begin to calculate the Standard deviation.
= 1’028. 1
= where ‘n’ is the sample size.
Standard Deviation Standard Deviation
Standard Deviation = 5.20146740429. Standard Deviation = 5.20 (to 2d.p.)
I will now do the same for the Broadsheet.
Total 830
Mean = 830 / 38 = 21.84
Now that I have found the mean, I can begin to calculate the Standard deviation.
= 2’149.54
= where ‘n’ is the Sample Size
Standard Deviation Standard Deviation
Standard Deviation = 7.52109314563. Standard Deviation = 7.52 (to 2 d.p.)
Conclusion
For my main investigation, I made several hypothesises, however I was disproved in saying that the Broadsheet would have an ‘overall’ higher sentence length. My results show that I was correct in saying that the broadsheet would have a greater dispersion of sentence lengths. Almost every method I employed proved that the Tabloid had a more consistent sentence length.
Upon making my hypothesis, I thought that the Broadsheet newspaper would use varied sentence lengths, as their readers would be able to cope, whereas in the Sun, they focused on shorter, more manageable sentences, to encourage their wide market. This was proved in the frequency polygon as the shorter sentences had a higher frequency, and the line dropped dramatically towards the longer sentences.
Finally, I think the Sun was more consistent overall, as the reporters are usually settled into a style of writing. The Guardian used informative detailed language, in comparison to the sun, where the journalist made opinions. This would make the Sun more varied dependant on the thoughts of the person, as he/she would be thinking off the top of their heads rather than structuring an article. It is apparent that the tabloid only briefly comments on the news/articles whereas the broadsheet goes into great depths.
This investigation may not be 100% accurate. This may be because of many things, I solely was responsible for data collection, and although I checked for mistakes, many may have been overlooked. A disadvantage that I had was that I only looked at one tabloid and one broadsheet. The newspapers that I selected may not be typical of those kinds of paper, so it would have been an advantage to sample more papers. If I were to repeat this investigation, or extend it I would sample more newspapers, however it was not possible to do it this time because it would be so time-consuming. If it were feasible to collect data like this for many samples, then I’d plot an accurate graph for the means of the means of the sample, which would be normally distributed, as long as the sample were large enough – The Central Limit Theorem states that ‘If the sample size is large enough then the distribution of the sample means is approximately Normal, irrespective of the distribution of the parent population.’ It would then be easier to predict more accurately the mean of the data.
